Breakdown of the semiclassical approximation during the early stages of preheating

The validity of the semiclassical approximation is investigated during the preheating phase in models of chaotic inflation using a modification of a criterion previously proposed for semiclassical gravity. If the modified criterion is violated then fluctuations of the two-point function for the quantum elds are large and the semiclassical approximation is not valid. Evidence is provided that the semiclassical approximation breaks down during the early stages of preheating, well before either scattering effects or backreaction effects are important

Sufficient conditions for regularity, positive recurrence, and absorption in level‐dependent QBD processes and related block‐structured Markov chains

This paper is concerned with level-dependent quasi-birth-death (LD-QBD) processes, i.e., multi-variate Markov chains with a block-tridiagonal -matrix, and a more general class of block-structured Markov chains, which can be seen as LD-QBD processes with total catastrophes. Arguments from univariate birth-death processes are combined with existing matrix-analytic formulations to obtain sufficient conditions for these block-structured processes to be regular, positive recurrent, and absorbed with certainty in a finite mean time. Specifically, it is our purpose to show that, as is the case for competition processes, these sufficient conditions are inherently linked to a suitably defined birth-death process. Our results are exemplified with two Markov chain models: a study of target cells and viral dynamics and one of kinetic proof-reading in T cell receptor signal transduction

The Inflationary Perturbation Spectrum

Motivated by the prospect of testing inflation from precision cosmic microwave background observations, we present analytic results for scalar and tensor perturbations in single-field inflation models based on the application of uniform approximations. This technique is systematically improvable, possesses controlled error bounds, and does not rely on assuming the slow-roll parameters to be constant. We provide closed-form expressions for the power spectra and the corresponding scalar and tensor spectral indices.Comment: 4 pages, 1 figur

Small-scale properties of the KPZ equation and dynamical symmetry breaking

A functional integral technique is used to study the ultraviolet or short distance properties of the Kardar-Parisi-Zhang (KPZ) equation with white Gaussian noise. We apply this technique to calculate the one-loop effective potential for the KPZ equation. The effective potential is (at least) one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, but non-renormalizable in 4 or higher space dimensions. This potential is intimately related to the probability distribution function (PDF) for the spacetime averaged field. For the restricted class of field configurations considered here, the KPZ equation exhibits dynamical symmetry breaking (DSB) via an analog of the Coleman-Weinberg mechanism in 1 and 2 space dimensions, but not in 3 space dimensions.Comment: V2 --- 6 pages, LaTeX 209, ReV_TeX 3.2. Title changed, presentation clarified, additional discussion added, references updated. No significant changes in physics conclusions. This version to appear in Physics Letters

Fate of a Naive T Cell: A Stochastic Journey

The homeostasis of T cell populations depends on migration, division and death of individual cells (1). T cells migrate between spatial compartments (spleen, lymph nodes, lung, liver, etc.), where they may divide or differentiate, and eventually die (2). The kinetics of recirculation influences the speed at which local infections are detected and controlled (3). New experimental techniques have been developed to measure the lifespan of cells, and their migration dynamics; for example, fluorescence-activated cell sorting (4), in vitro time-lapse microscopy (5), or in vivo stable isotope labeling (e.g., deuterium) (6). When combined with mathematical and computational models, they allow estimation of rates of migration, division, differentiation and death (6, 7). In this work, we develop a stochastic model of a single cell migrating between spatial compartments, dividing and eventually dying. We calculate the number of division events during a T cell's journey, its lifespan, the probability of dying in each compartment and the number of progeny cells. A fast-migration approximation allows us to compute these quantities when migration rates are larger than division and death rates. Making use of published rates: (i) we analyse how perturbations in a given spatial compartment impact the dynamics of a T cell, (ii) we study the accuracy of the fast-migration approximation, and (iii) we quantify the role played by direct migration (not via the blood) between some compartments

Acoustic geometry for general relativistic barotropic irrotational fluid flow

"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the literature are based on non-relativistic barotropic irrotational fluids, defined in a flat Newtonian background. The extension, first to special relativistic barotropic fluid flow, and then to general relativistic barotropic fluid flow in an arbitrary background, is less straightforward than it might at first appear. In this article we provide a pedagogical and simple derivation of the general relativistic "acoustic spacetime" in an arbitrary (d+1) dimensional curved-space background.Comment: V1: 23 pages, zero figures; V2: now 24 pages, some clarifications, 2 references added. This version accepted for publication in the New Journal of Physics. (Special issue on "Classical and Quantum Analogues for Gravitational Phenomena and Related Effects"

Zeta functions, renormalization group equations, and the effective action

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley--DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action, and use this to derive the leading-logarithms in the one-loop effective action for arbitrary quantum field theories.Comment: 4 pages, ReV-TeX 3.

Short distance and initial state effects in inflation: stress tensor and decoherence

We present a consistent low energy effective field theory framework for parameterizing the effects of novel short distance physics in inflation, and their possible observational signatures in the Cosmic Microwave Background. We consider the class of general homogeneous, isotropic initial states for quantum scalar fields in Robertson-Walker (RW) spacetimes, subject to the requirement that their ultraviolet behavior be consistent with renormalizability of the covariantly conserved stress tensor which couples to gravity. In the functional Schr\"odinger picture such states are coherent, squeezed, mixed states characterized by a Gaussian density matrix. This Gaussian has parameters which approach those of the adiabatic vacuum at large wave number, and evolve in time according to an effective classical Hamiltonian. The one complex parameter family of $\alpha$ squeezed states in de Sitter spacetime does not fall into this UV allowed class, except for the special value of the parameter corresponding to the Bunch-Davies state. We determine the finite contributions to the inflationary power spectrum and stress tensor expectation value of general UV allowed adiabatic states, and obtain quantitative limits on the observability and backreaction effects of some recently proposed models of short distance modifications of the initial state of inflation. For all UV allowed states, the second order adiabatic basis provides a good description of particles created in the expanding RW universe. Due to the absence of particle creation for the massless, minimally coupled scalar field in de Sitter space, there is no phase decoherence in the simplest free field inflationary models. We apply adiabatic regularization to the renormalization of the decoherence functional in cosmology to corroborate this result.Comment: 83 pages, 2 figures, minor changes in content and styl

Tumor growth instability and the onset of invasion

Motivated by experimental observations, we develop a mathematical model of chemotactically directed tumor growth. We present an analytical study of the model as well as a numerical one. The mathematical analysis shows that: (i) tumor cell proliferation by itself cannot generate the invasive branching behaviour observed experimentally, (ii) heterotype chemotaxis provides an instability mechanism that leads to the onset of tumor invasion and (iii) homotype chemotaxis does not provide such an instability mechanism but enhances the mean speed of the tumor surface. The numerical results not only support the assumptions needed to perform the mathematical analysis but they also provide evidence of (i), (ii) and (iii). Finally, both the analytical study and the numerical work agree with the experimental phenomena.Comment: 12 pages, 8 figures, revtex